Magnetic resonance imaging is an imaging method which magnetically excites nuclear spins of a patient placed in a static magnetic field with an RF signal at the Larmor frequency to reconstruct an image using a magnetic resonance signal resulting from the excitation.
An HFI (Half Fourier Imaging) method is known in the field of magnetic resonance imaging, The HFI method, which uses complex symmetry of data in k-space, fills those regions of the k-space in which data has not been collected with data based on collected k-space data and thereby constructs an image.
Also, in the field of magnetic resonance imaging, PI (parallel imaging) is known as a high-speed imaging technique which uses differences in the sensitivity distributions for RF magnetic fields of multiple coil elements. PI is an imaging method which receives echo data using the multiple coil elements, makes a phase-encoding step size larger than normal, and thereby reduces the number of phase-encoding lines needed for image reconstruction. Consequently, the use of PI makes it possible to reduce imaging time greatly. Specifically, it is only necessary to collect data of approximately half a specified number of phase-encoding lines. Thus, the imaging time is cut almost in half.
When echo data is collected during parallel imaging, folded intermediate image data is generated for each channel corresponding to each coil element. Then, an unfolding process is applied to multiple items of intermediate image data corresponding in number to the number of channels to remove folding, and consequently a single set of unfolded final image data is generated. RF magnetic field (B1) sensitivity distribution data of each coil element is used in the unfolding process.
Conventionally, parallel imaging which uses multiple coil elements employs half Fourier imaging.
FIG. 1 is a flowchart showing conventional data processing procedures in which PI and HFI are used in conjunction.
As shown in Step S1 in FIG. 1, an HFI process is performed to fill in data not collected in the k-space based on k-space data collected by PI on a channel-by-channel basis. Consequently, folded intermediate image data is generated for each channel.
The HFI process is performed as follows.
First, as shown by expression (1-1) and expression (1-2), a filtering process fh using a Homodyne filter and filtering process fl using a low-pass filter are performed on k-space data K(i) collected by coil elements i (i=1, 2, 3, . . . , Nch), and k-space data Kh(i) filtered through the Homodyne filter and k-space data Kl(i) filtered through the low-pass filter are generated.K(i)*fh→Kh(i)  (1-1) (Step S11)K(i)*fl→Kl(i)  (1-2) (Step S11)
Next, as shown by expression (2-1) and expression (2-2), inverse fast Fourier transforms (IFFTs) are performed on the k-space data Kh(i) filtered through the Homodyne filter and k-space data Kl(i) filtered through the low-pass filter, and consequently folded intermediate image data Vh(i) and Vl(i) are generated as real space (R-space) data.IFFT(Kh(i))→Vh(i)  (2-1) (Step S12)IFFT(Kl(i))→Vl(i)  (2-2) (Step S12)
In Step S13, the number of iterations of the HFI process is checked, and if the number of iterations is less than a predetermined number M, the flow goes to Step S14.
In Step S14, a phase correction process is performed using expression (3), and consequently intermediate image data V(i) is generated for each coil element i.V(i)=2·Real part{Vh(i)*Vl(i)/|Vl(i)|}  (3) (Step S14)
In Step S15, fast Fourier transforms (FFTs) are performed on the intermediate image data V(i) subjected to the phase correction process, and consequently the real space data is reconverted into k-space data FFT(V(i)). The resulting k-space data FFT(V(i)) is full k-space data, meaning that those regions of the k-space from which data was not collected have been filled with data. This is due to the filtering process (Step S11) and inverse Fourier transform process (Step S12), through which a data filling process is performed indirectly. However, at this stage, accuracy of the data in the filled regions is not necessarily high. Next, the k-space data FFT(V(i)) and collected k-space data K(i) undergo weighted addition using a weighting coefficient α.K(i)=α*FFT(V(i))+(1−α)*K(i)  (4) (Step S16)
Results of the weighted addition is used as k-space data K(i) to calculate intermediate image data V(i) again and the HFI process represented by expressions (1-1), (1-2), (2-1), (2-2), (3), and (4) is repeated a predetermined number M of iterations (e.g., 2 to 4 times) to improve accuracy of the filling process in the k-space. That is, the processes from Step S11 to Step S16 including the phase correction process and data filling process—i.e., the HFI process according to the present embodiment—are repeated the predetermined number of times.
Next, in Step S2, an unfolding process is performed on the channel-by-channel intermediate image data Vh(i) and Vl(i) obtained using expressions (2-1) and (2-2). That is, as shown by expressions (5-1) and expression (5-2), unfolded MR pixel values xh and xl at position Npt are found as respective vectors from imaging signal strengths yh and yl given by respective vectors whose components are Nch items of intermediate image data Vh(i) and Vl(i), respectively, as well as from an Nch×Npt sensitivity matrix S which represents sensitivity at the position Npt of each coil element i.xh=(SHS)−1SHyh  (5-1)xl=(SHS)−1SHyl  (5-2)
where
yh={Vh(1), Vh(2), . . . , Vh(Nch)}
yl={Vl(1), Vl(2), . . . , Vl(Nch)}
xh={Vh_unfold(1), Vh_unfold(2), . . . , Vh_unfold(Npt)
xl={Vl_unfold(1), Vl_unfold(2), . . . , Vl_unfold(Npt)}
SH is a transposed complex conjugate matrix of the matrix S.
When components of the MR pixel value vectors xh and xl are positioned, unfolded image data Vh_unfold and Vl_unfold without folding are generated, respectively.
Next, in Step S3, the image data Vh_unfold and Vl_unfold are subjected to the phase correction process given by expression (6) to generate final image data Vfinal.Vfinal=2·Real part{Vh_unfold*Vl_unfold/|Vl_unfold|}  (6)
Subsequently, image processing such as distortion correction is applied as required (Step S4). However, when PI and HFI are used in conjunction, conventional processing methods need to perform the HFI process repeatedly on a channel-by-channel basis to improve the accuracy of the filling process in the k-space. Consequently, the number of times the HFI process is repeated equals the number of channels×the number of iterations, resulting in increased amounts of data processing and data processing time. Therefore, there is demand to reduce the amounts of data processing and data processing time.